Function Repository Resource:

# TetrahelixMesh

Generate a mesh region representing the tetrahelix

Contributed by: Jan Mangaldan
 ResourceFunction["TetrahelixMesh"][n,s] gives a mesh region representing the Boerdijk–Coxeter tetrahelix made from n regular tetrahedra of unit edge length, with s set to 1 for the counterclockwise orientation or -1 for the clockwise orientation. ResourceFunction["TetrahelixMesh"][n] gives a mesh region representing an counterclockwise tetrahelix.

## Details

ResourceFunction["TetrahelixMesh"] is also known as the Boerdijk–Coxeter helix.
The tetrahelix is a linear stacking of regular tetrahedra, arranged so that the edges of the complex that belong to only one tetrahedron form three intertwined helices.
ResourceFunction["TetrahelixMesh"] takes the same options as MeshRegion.

## Examples

### Basic Examples (2)

A tetrahelix with 10 tetrahedra, oriented counterclockwise:

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A tetrahelix with 10 tetrahedra, oriented clockwise:

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### Scope (2)

Use MeshRegion options to change the style:

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Compute the volume and surface area of the helix:

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These can be expressed in terms of the volume and surface area of a single tetrahedron:

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### Properties and Relations (3)

Use TransformedRegion to rescale or translate the tetrahelix:

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Use MeshConnectivityGraph to obtain a Graph representation of the tetrahelix:

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The tetrahelix can be inscribed inside a cylinder with radius , and a cylinder of radius can be inscribed in the helix:

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### Neat Examples (1)

Visualize a helical sphere packing:

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## Version History

• 1.0.0 – 21 June 2021